There are a lot of blogs who has posted about this. i am not posting any link here for I may get a warning here, but all you need to do is to search Google for query "connect iphone 4 with apple tv" and you will see your required results on the first page of Google!

nope, you'll see a dozen links talking about connecting the iPhone 4 with OS below 5.0 nothing on new OS. Not to mention the fact that i am not interested in connecting to an Apple TV, I want to connect to a normal TV.

I've noticed that since OS 5 has been released that there is no longer the TV-OUT option listed under the settings menu...

While I can't speak to whether being jailbroken would affect normal functionality (it shouldn't, but you never know with the wide variety of hacks out there), you should still be able to connect the cables and they should "just work" -- they definitely do for me on all of my iOS 5.1.1 devices, including an iPhone 4.

The big change in iOS 5.1 is that the TV Out option is now hidden unless you plug in a video output cable, and when it does appear, it's now on the Settings, General menu (right below "iTunes Wi-Fi Sync"). The feature otherwise works the same as it did in prior iOS versions, however.